Verify the property of multiplication a= ab+ ac for the rational numbers a=-3/4 b=2/3 c=15/24
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Answer:
We will learn the properties of multiplication of rational numbers i.e. closure property, commutative property, associative property, existence of multiplicative identity property, existence of multiplicative inverse property, distributive property of multiplication over addition and multiplicative property of 0.
Closure property of multiplication of rational numbers:
The product of two rational numbers is always a rational number.
If a/b and c/d are any two rational numbers then (a/b × c/d) is also a rational number.
For example:
(i) Consider the rational numbers 1/2 and 5/7. Then,
(1/2 × 5/7) = (1 × 5)/(2 × 7) = 5/14, is a rational number .
(ii) Consider the rational numbers -3/7 and 5/14. Then
(-3/7 × 5/14) = {(-3) × 5}/(7 × 14) = -15/98, is a rational number .
(iii) Consider the rational numbers -4/5 and -7/3. Then
(-4/5 × -7/3) = {(-4) × (-7)}/(5 × 3) = 28/15, is a rational number.
Commutative property of multiplication of rational numbers:
Two rational numbers can be multiplied in any order.
Thus, for any rational numbers a/b and c/d, we have:
(a/b × c/d) = (c/d × a/b)
For example:
(i) Let us consider the rational numbers 3/4 and 5/7 Then,
(3/4 × 5/7) = (3 × 5)/(4 × 7) = 15/28 and (5/7 × 3/4) = (5 × 3)/(7 × 4)
= 15/28
Therefore, (3/4 × 5/7) = (5/7 × 3/4)
(ii) Let us consider the rational numbers -2/5 and 6/7.Then,
{(-2)/5 × 6/7} = {(-2) × 6}/(5 × 7) = -12/35 and (6/7 × -2/5 )
= {6 × (-2)}/(7 × 5) = -12/35
Therefore, (-2/5 × 6/7 ) = (6/7 × (-2)/5)
(iii) Let us consider the rational numbers -2/3 and -5/7 Then,
(-2)/3 × (-5)/7 = {(-2) × (-5) }/(3 × 7) = 10/21 and (-5/7) × (-2/3)
= {(-5) × (-2)}/(7 × 3) = 10/21
Therefore, (-2/3) × (-5/7) = (-5/7) × (-2)/3
Answer:
Verify the property of multiplication a= ab+ ac for the rational numbers a=-3/4 b=2/3 c=15/24
Step-by-step explanation:
Verify the property of multiplication a= ab+ ac for the rational numbers a=-3/4 b=2/3 c=15/24